Z-transform implementation of digital watermarks

ABSTRACT

Z-transform calculations may be used to encode (and/or decode) carrier signal independent data (e.g., digital watermarks) to a digital sample stream. Deterministic and non-deterministic components of a digital sample stream signal may be analyzed for the purposes of encoding carrier signal independent data to the digital sample stream. The carrier signal independent data may be encoded in a manner such that it is restricted or concentrated primarily in the non-deterministic signal components of the carrier signal. The signal components can include a discrete series of digital samples and/or a discreet series of carrier frequency sub-bands of the carrier signal. Z-transform calculations may be used to measure a desirability of-particular locations and a sample stream in which to encode the carrier signal independent data.

RELATED APPLICATIONS

This application relates to U.S. patent application Ser. No. 08/489,172filed on Jun. 7, 1995, U.S. patent application Ser. No. 08/587,944 filedon Jan. 17, 1996, U.S. patent application Ser. No. 08/587,943 filed onJan. 16, 1996, and U.S. patent application Ser. No. 08/677,435 filed onJul. 2, 1996. Each of these related applications is incorporated hereinby reference in their entirety.

BACKGROUND OF THE INVENTION

Digital distribution of multimedia content (audio, video, etc.) and theimpending convergence of industries that seek to make this goal areality (computer, telecommunications, media, electric power, etc.)collide with the simplicity of making perfect digital copies. Thereexists a vacuum in which content creators resist shifts to full digitaldistribution systems for their digitized works, due to the lack of ameans to protect the copyrights of these works. In order to make suchcopyright protection possible, there must exist a mechanism todifferentiate between a master and any of its derivative copies. Theadvent of digital watermarks makes such differentiation possible. Withdifferentiation, assigning responsibility for copies as they aredistributed can assist in the support and protection of underlyingcopyrights and other “neighboring rights,” as well as, theimplementation of secure metering, marketing, and other as yet stillundecided applications. Schemes that promote encryption, cryptographiccontainers, closed systems, and the like attempt to shift control ofcopyrights from their owners to third parties, requiring escrow ofmasters and payment for analysis of suspect, pirated copies. Aframe-based, master-independent, multi-channel watermark system isdisclosed in U.S. patent application Ser. No. 08/489,172 filed on Jun.7, 1995 and entitled “STEGANOGRAPHIC METHOD AND DEVICE”, U.S. patentapplication Ser. No. 08/587,944 filed on Jan. 17, 1996 and entitled“METHOD FOR HUMAN-ASSISTED RANDOM KEY GENERATION AND APPLICATION FORDIGITAL WATERMARK SYSTEM”, and U.S. patent application Ser. No.08/587,943 filed on Jan. 16. 1996 and entitled “METHOD FOR STEGA-CIPHERPROTECTION OF COMPUTER CODE”. These applications describe methods bywhich copyright holders can watermark and maintain control over theirown content. Any suspect copies carry all necessary copyright or other“rights” information within the digitized signal and possession of anauthorized “key” and the software (or even hardware) described in theseapplications would make determination of ownership or other importantissues a simple operation for the rights holder or enforcer.

Optimizing watermark insertion into a given signal is further describedin the U.S. patent application Ser. No. 08/677,435 filed on Jul. 2, 1996and entitled “OPTIMIZATION METHODS FOR THE INSERTION, PROJECTION ANDDETECTION OF DIGITAL WATERMARKS IN DIGITIZED DATA”. This applicationdiscloses accounting for the wide range of digitally-sampled signalsincluding audio, video, and derivations thereof that may constitute a“multimedia” signal. The optimization techniques described in thatapplication take into account the two components of all digitizationsystems: error coding and digital filters. The premise is to provide abetter framework or definition of the actual “aesthetic” that comprisesthe signal being reproduced, whether through commercial standards ofoutput (NTSC, CD-quality audio, etc.) or lossless and lossy compression(MPEG-2, Perceptual Audio Coding, AC-3, Linear Adaptive Coding, and thelike), so that a watermark may be targeted at precisely the part of thesignal comprising such an “aesthetic” in order that it be as robust aspossible (i.e., difficult to remove without damaging the perceptualquality of the signal). However the content is stored, the signal stillcarries the digital watermark. Additionally, transmission media may becharacterized as a set of “filters” that may be pre-analyzed todetermine the best “areas” of the signal in which watermarks “should” beencoded, to preserve watermarks in derivative copies and ensure maximumdestruction of the main, carrier signal when attempts are made to eraseor alter the watermarked content.

Optimal planning of digital watermark insertion can be based on theinversion of digital filters to establish or map areas comprising agiven content signal's “insertion envelope.” That is, the results of thefilter operation are considered in order to “back out” a solution. Inthe context of this discussion, the phrase “inverting” a filter maymean, alternatively, mathematical inversion, or the normal computationof the filter to observe what its effect would be, were that filterapplied at a later time. Planning operations will vary for givendigitized content: audio, video, multimedia, etc. Planning will alsovary depending on where a given “watermarker” is in the distributionchain and what particular information needs that user has in encoding agiven set of information fields into the underlying content. Thedisclosures described take into account discrete-time signal processingwhich can be accomplished with Fast Fourier Transforms that arewell-known in the art of digital signal processing. Signalcharacteristics are also deemed important: a specific method foranalysis of such characteristics and subsequent digital watermarking isdisclosed in further detail in this application. The antecedents of thepresent invention cover time and frequency domain processing, which canbe used to examine signal characteristics and make modifications to thesignal. A third way would be to process with z-transforms that canestablish signal characteristics in a very precise manner over discreteinstances of time. In particular, z-transform calculations can be usedto separate the deterministic, or readily predictable, components of asignal from the non-deterministic (unpredictable or random) components.It should be apparent to those skilled in the art that non-deterministicis a subjective term whose interpretation is implicitly affected byprocessing power, memory, and time restrictions. With unlimited DSP(digital signal processing) power, memory, and time to process, we mighttheoretically predict every component of a signal. However, practicalityimposes limitations. The results of the z-transform calculations willyield an estimator of the signal in the form of a deterministicapproximation. The difference between a signal reconstituted from thedeterministic estimator and the real signal can be referred to as error,and the error in an estimator can be further analyzed for statisticalcharacteristics. Those skilled in the art will be aware that LinearPredictive Coding (LPC) techniques make use of these properties. So theerror can be modeled, but is difficult to reproduce exactly fromcompressed representations. In essence, this error represents therandomness in a signal which is hard to compress or reproduce, but infact may contribute significantly to the gestalt perception of thesignal.

The more elements of error determined with z-transforms, the better ablea party is at determining just what parts of a given carrier signal aredeterministic, and thus predictable, and what elements are random. Theless predictable the watermark-bearing portion of a signal is and themore it contributes to the perception of the signal, as previouslydisclosed, the more secure a digital watermark can be made. Z-transformanalysis would disclose just which phase components are deterministicand which are random. This is because it is difficult to compress orotherwise remove unpredictable signal components. Error analysis furtherdescribes the existence of error function components and would reliablypredict what signals or data may later be removed by additionalz-transform analysis or other compression techniques. In effect, theerror analysis indicates how good an approximation can be made, anotherway of stating how predictable a signal is, and by implication, how muchrandomness it contains. Z-transforms are thus a specialized means tooptimize watermark insertion and maximize the resulting security ofencoded data from attempts at tampering The results of a Z-transform ofinput samples could be analyzed to see “exactly” how they approximatethe signal, and how much room there is for encoding watermarks in amanner that they will not be removed by compression techniques whichpreserve a high degree of reproduction quality.

Time is typically described as a single independent variable in signalprocessing operations but in many cases operations can be generalized tomultidimensional or multichannel signals. Analog signals are definedcontinuously over time, while digital signals are sampled at discretetime intervals to provide a relatively compact function, suitable forstorage on a CD, for instance, defined only at regularly demarcatedintervals of time. The accrued variables over time provide adiscrete-time signal that is an approximation of the actual non-discreteanalog signal. This discreteness is the basis of a digital signal. Iftime is unbounded and the signal comprises all possible values, acontinuous-valued signal results. The method for converting acontinuous-valued signal into a discrete time value is known assampling. Sampling requires quantization and quantization implies error.Quantization and sampling are thus an approximation process.

Discreteness is typically established in order to perform digital signalprocessing. The issue of deterministic versus random signals is based onthe ability to mathematically predict output values of a signal functionat a specific time given a certain number of previous outputs of thefunction. These predictions are the basis of functions that canreplicate a given signal for reproduction purposes. When suchpredictions are mathematically too complicated or are not reasonablyaccurate, statistical techniques may be used to describe theprobabalistic characteristics of the signal. In many real worldapplications, however, determinations of whether a signal, or part of asignal, is indeed random or not is difficult at best. The watermarksystems described in earlier disclosures mentioned above have a basis inanalyzing signals so that analysis of discrete time frames can be madeto insert information into the signal being watermarked. When signalcharacteristics are measured, a key factor in securely encoding digitalwatermarks is the ability to encode data into a carrier signal in a waythat mimics randomness or pseudo randomness so that unauthorizedattempts at erasing the watermark necessarily require damage to thecontent signal. Any randomness that exists as a part of the signal,however, should be estimated in order that a party seeking to optimallywatermark the input signal can determine the best location for watermarkinformation and to make any subsequent analysis to determine thelocation of said watermarks more difficult. Again, typicalimplementations of signal processing that use z-transforms seek todescribe what parts of the signal are deterministic so that they may bedescribed as a compact, predictable function so that the signal maybefaithfully reproduced. This is the basis for so-called linear predictivecoding techniques used for compression. The present invention isconcerned with descriptions of the signal to better define just whatparts of the signal are random so that digital watermarks may beinserted in a manner that would make them more or less tamperproofwithout damage to the carrier signal. Additional goals of the system aredynamic analysis of a signal at discrete time intervals so thatwatermarks may be dynamically adjusted to the needs of users in suchinstances as on-the-fly encoding of watermarks or distribution viatransmission media (telephone, cable, electric powerlines, wireless,etc.)

Signal characteristics, if they can be reasonably defined, are alsoimportant clues as to what portion or portions of a given signalcomprise the “aesthetically valuable” output signal commonly known asmusic or video. As such, perceptual coding or linear predictive codingis a means to accurately reproduce a signal, with significantcompression, in a manner that perfectly replicates the original signal(lossless compression) or nearly replicates the signal (lossycompression). One tool to make better evaluations of the underlyingsignal includes the class of linear time-invariant (LTI) systems. Aspointed out in Digital Signal Processing (Principles, Algorithms, andApplications), 3rd Ed. (Proakis and Manolakis), (also Practical DSPModeling, Techniques, and Programming in C by Don Morgan) thez-transform makes possible analysis of a continuous-time signal in thesame manner as discrete-time signals because of the relationship between“the convolution of two time domain signals is equivalent tomultiplication of their corresponding z-transforms.” It should be clearthat characterization and analysis of LTI systems is useful in digitalsignal processing; meaning DSP can use a z-transform and invert thez-transform to deterministically summarize and recreate a signal's timedomain representation. Z-transforms can thus be used as a mathematicalway in which to describe a signal's time domain representation wherethat signal may not be readily processed by means of a Fouriertransform. A goal of the present invention is to use such analysis so asto describe optimal locations for watermarks in signals which typicallyhave components both of deterministic and non-deterministic (predictableand unpredictable, respectively) nature. Such insertion would inherentlybenefit a system seeking to insert digital watermarks, that containsensitive information such as copyrights, distribution agreements,marketing information, bandwidth rights, more general “neighboringrights,” and the like, in locations in the signal which are not easilyaccessible to unauthorized parties and which cannot be removed withoutdamaging the signal. Such a technique for determining watermark locationwill help ensure “pirates” must damage the content in attempts atremoval, the price paid without a legitimate “key.”

Some discussion of proposed systems for frequency-based encoding of“digital watermarks” is necessary to differentiate the antecedents ofthe present invention which processes signals frame-by-frame and mayinsert information into frequencies without requiring the resultingwatermark to be continuous throughout the entire clip of the signal.U.S. Pat. No. 5,319,735 to Preuss et al. discusses a spread spectrummethod that would allow for jamming via overencoding of a “watermarked”frequency range and is severely limited in the amount of data that canbe encoded—4.3 8-bit symbols per second. Randomization attacks will notresult in audible artifacts in the carrier signal, or degradation of thecontent as the information signal is subaudible due to frequencymasking. Decoding can be broken by a slight change in the playbackspeed. It is important to note the difference in application betweenspread spectrum in military field use for protection of real-time radiosignals versus encoding information into static audio files. In theprotection of real-time communications, spread spectrum has anti-jamfeatures since information is sent over several channels at once, and inorder to jam the signal, you have to jam all channels, including yourown. In a static audio file, however, an attacker has all the time andprocessing power in the world to randomize each sub-channel in thesignaling band with no penalty to themselves, so the anti-jam featuresof spread spectrum do not extend to this domain if the encoding issub-audible. Choosing where to encode in a super-audible range of thefrequency, as is possible with the present invention's antecedents, canbetter be accomplished by computing the z-transforms of the underlyingcontent signal, in order to ascertain the suitability of particularlocations in the signal for watermark information.

Instead of putting a single subaudible, digital signature in a sub-bandas is further proposed by such entities as NEC, IBM, Digimarc, and MITMedia Lab, the antecedent inventions' improvement is its emphasis onframe-based encoding that can result in the decoding of watermarks fromclips of the original full signal (10 seconds, say, of a 3 minute song).With signatures described in MIT's PixelTag or Digimarc/NEC proposals,clipping of the “carrier signal” (presently only based on results fromtests on images, not video or audio signals which have time domains),results in clipping of the underlying watermark. Additionally, thepresent invention improves on previous implementations by providing analternative computational medium to time/amplitude or frequency/energydomain (Fourier Transform) calculations and providing an additionalmeasure by which to distinguish parts of a signal which are bettersuited to preserve watermarks through various DSP operations and forcedamage when attempts at erasure of the watermarks are undertaken.Further, the necessity of archiving or putting in escrow a master copyfor comparison with suspect derivative copies would be unnecessary withthe present invention and its proposed antecedents. Further, statisticaltechniques, not mathematical formulas, that are used to determine a“match” of a clip of a carrier signal to the original signal, bothuneconomical and unreasonable, would not be necessary to establishownership or other information about the suspect clip. Even if suchtechniques or stochastic processes are used, as in an audiospread-spectrum-based watermarking system being proposed by Thorn-EMI'sCRL, called ICE, the further inability to decode a text file or othersimilar file that has been encoded using a watermark system aspreviously disclosed by above-mentioned U.S. patent applicationsincluding “Steganographic Method and Device”, “Method for Human-AssistedRandom Key Generation and Application for Digital Watermark System”,“Method for Stega-cipher Protection of Computer Code”, and “OptimalMethods for the Insertion, Protection and Detection of DigitalWatermarks in Digitized Data”, where all “watermark information” residesin the derivative copy of a carrier signal and its clips (if there hasbeen clipping), would seem archaic and fail to suit the needs ofartists, content creators, broadcasters, distributors, and their agents.Indeed, reports are that decoding untampered watermarks with ICE in anaudio file experience “statistical” error rates as high as 40%. This isa poor form of “authentication” and fails to establish more clearly“rights” or ownership over a given derivative copy. Human listeningtests would appear a better means of authentication versus such“probabalistic determination”. This would be especially true if suchsystems contain no provision to prevent purely random false-positiveresults, as is probable, with “spread spectrum” or similar “embeddedsignaling”—type “watermarks,” or actually, with a better definition,frequency-based, digital signatures.

SUMMARY OF THE INVENTION

The present invention relates to a method of using z-transformcalculations to encode (and/or

The present invention additionally relates to a method of usingz-transform calculations to determine portions of a signal which may besuccessfully compressed or eliminated using certain processingtechniques, without adverse impact on signal quality.

The present invention additionally relates to a method of encoding adigital watermark into a digital sample stream such that the watermarkinformation is carried entirely in the most non-deterministic portionsof the signal.

DETAILED DESCRIPTION

The Z-transform is a way of describing the characteristics of a signal.It is an alternative to time/amplitude and frequency/energy domainmeasures which expresses an estimate of periodic components of adiscrete signal. In a digital signal processing environment, a samplingtheorem, known specifically as the Nyquist Theorem, proves that bandlimited signals can be sampled, stored, processed, transmitted,reconstructed, desampled or processed as discrete values. For thetheorem to hold, the sampling must be done at a frequency that is twicethe frequency of the highest signal frequency one seeks to capture andreproduce. The time and frequency domains are thus implicitly importantin developing functions that can accurately replicate a signal. In athird domain, the z-transform enables analysis of the periodic nature ofdecode) independent data (e.g., digital watermark data) to a digitalsample stream.

The present invention additionally relates to a method of analyzingdeterministic and non-deterministic components of a signal comprised ofa digital sample stream. Carrier signal independent data is encoded inthe digital sample stream and encoding of the carrier signal independentdata is implemented in a manner such that it is restricted to orconcentrated primarily in the non-deterministic signal components of thecarrier signal. The signal components can include a discrete series ofdigital samples and/or a discrete series of frequency sub-bands of thecarrier signal.

The present invention additionally relates to a method of usingz-transform calculations to measure a desirability of particularlocations of a sample stream in which to encode carrier signalindependent data. The desirability includes a difficulty in predicting acomponent of the sample stream at a given location which can be measuredby the error function. The component and location may be comprised ofinformation regarding at least one of the following: wave, amplitude,frequency, band energy, and phase energy. The present inventionadditionally relates to a method of encoding digital watermarks atvarying locations in a sample stream with varying envelope parameters.discrete-time signals (and linear time-invariant systems) much as theLaplace transform plays a role in the analysis of continuous-timesignals (and linear time-invariant systems). The difference is that thez-transform expresses results on the so-called z-plane, an imaginarymathematical construct which may be thought of as a Cartesian coordinatesystem with one axis replaced by imaginary numbers (numbers expressed inrelation to the square root of −1). This may allow manipulations ofsignals which are not possible with Fourier Transform analyses (thefrequency/energy domain). At the least, the z-transform is analternative way to represent a signal. The imaginary number axis servesas a representation of the phase of the signal, where the phaseoscillates through an ordered, bounded set of values over a potentiallyinfinite series of discrete time values. Phase is the framework forrepresenting the periodic nature of the signal. This third method ofdescribing a discrete-time signal has the property of equating theconvolution of two time-domain signals in the result of themultiplication of those signals' corresponding z-transforms. Byinverting a z-transform, the time-domain representation of the signalmay be approximately or wholly reconstructed.

To better define the z-transform, it is a power series of adiscrete-time signal and is mathematically described hence:${X(z)} = {\overset{\infty}{\sum\limits_{n = {- \infty}}}{{x(n)}z^{- n}}}$where,x(n) is a discrete-time signalX(z) is a complex plane representationz is a complex variable

Because the z-transform is an infinite power series, a region ofconvergence (ROC) is the set of all values of z where X(z) has a finitevalue, in other words, this is where the series has a computable value.Conversely, nonconvergence would mean randomness of the signal.

Where z=0 or z=∞, the series is unbounded and thus the z-plane cannot bedefined. What is required is a closed form expression that can only bedescribed with a region of convergence (ROC) being specified. Acoordinate in the imaginary z-plane can be interpreted to convey bothamplitude and phase information. Phase is closely related to frequencyinformation. Again, phase can be understood to oscillate at regularperiods over infinite discrete time intervals, and is used to expressinformation on the periodic nature of signals. Thus, as an alternativerepresentation of a signal, the z-transform helps describe how a signalchanges over time.

Some parameters of the region of convergence (ROC) necessitate theestablishment of the duration (finite versus infinite) and whether theROC is causal, anticasual, or two-sided. Special cases of signalsinclude one that has an infinite duration on the right side, but not theleft side; an infinite duration on the left side, but not the rightside; and, one that has a finite duration on both the right and leftsides—known, respectively, as right-sided, left-sided, andfinite-duration two-sided. Additionally, in order to correctly obtainthe time domain information of a signal from its z-transform, furtheranalysis is done. When a signals z-transform is known the signal'ssequence must be established to describe the time domain of the signal—aprocedure known as inverse z-transform, Cauchy integral theorem is aninversion formula typically used. Properties of the z-transform will nowbe described so that those skilled in the art are able to understand therange of computations in which z-transforms may be used for watermarkrelated calculations. Property Time Domain z-Domain ROC Notation x(n)X(z) ROC: r₂ < [z] < r₁ x₁(n) X₁(z) ROC₁ x₂(n) X₂(z) ROC₂ Linearitya₁x₁(n) + a₂x₂(n) a₁X₁(z) + a₂X₂(z) At least the intersection of ROC₁and ROC₂ Time shifting X(n − k) z^(−k)X(Z) That of X(z), except z = 0 ifk > 0 nd = ∞ if k > 0 Scaling in the z-domain a^(n)x(n) X(a⁻¹z) [a]r₂ <[z] < [a]r₁ Time reversal x(−n) X(z⁻¹) 1/r₁ < [z] < 1/r₂ Conjugationx*(n) X*(z*) ROC Real Part Re{x(n)} 1/2{X(z) + X*(z*)} Includes ROCImaginary Pail Im{x(n)} 1/2{X(z) − X*(z*)} Includes ROC Differential innx(n) −z(−z((dX(z)/(dz))} r₂ < [z] < r₁ the z-domain Convolution(x₁(n)) * (x2(n)) X₁(z)X₂(z) At least the intersection of ROC₁ and ROC₂Correlation rx₁x₂(1) = x₁(1) * x₂(−1) Rx₁x₂(z) = X₁(z)X₂(z⁻¹) At leastthe intersection of ROC of X₁(z) and X₂(z⁻¹) Initial value theorem Ifx(n) causal x(O) = lim X(z) Multiplication x₁(n)x₂(n)1/2πj{∫_(z  to  ∞)^(z  to  ∞)X₁(v)X₂((z/v)  v⁻¹𝕕v} At least r₁₁r₂₁ < [z]< r_(1u)r_(2u) Parseval's relation${\sum\limits^{\infty}{{X_{1}(n)}{X_{2}^{*}(n)}}} = {{1/2}{\pi j}\left\{ {\int{{X_{1}(v)}{X_{2}^{*}\left( \left( {1/v^{*}} \right)\quad \right.}v^{- 1}{\mathbb{d}v}}} \right\}}$Note:“[ ]” denote absolute values; For “Multiplication” and “Parseval'srelation” the “∫” is for “0_(c)” a circle in the ROC. From DigitalSignal Processing (Principles, Algorithms, and Applications) - 3rd Ed.Proakis & Manolakis

The inversion of the z-transform with three methods further described,in Digital Signal Processing (Principles, Algorithms, andApplications)—3rd Ed. Proakis & Manolakis, as 1) Direct evaluation bycontour integration 2) Expansion into a series of terms, in thevariables z, and z⁻¹ and 3) Partial-fraction expansion and table lookup.Typically the Cauchy theorem is used for direct evaluation. Indetermining causality, LTI systems are well-suited in establishing thepredictability of time-domain characteristics with pole-zero locations.For applications of digital watermarks as described in the presentinvention the importance of both alternatively describing a signal andestablishing deterministic characteristics of the signal's components isclear to those skilled in the art. Placing watermarks in the “random”parts of a signal, those that are difficult to predict and therebycompress, would enhance the security from attacks by pirates seeking toidentify the location of said watermarks or erase them without knowingtheir specific location. Use of z-transforms to establish a more secure“envelope” for watermark insertion works to the advantage of thoseseeking to prevent such attacks. Similarly, creation of linearpredictive coding filters is an excellent example that benefits frompreanalysis of content signals prior to the insertion of watermarks.

This is an extension of the application of optimal filter design forapplications for frame-based watermark systems as described in theabove-mentioned patent applications entitled “STEGANOGRAPHIC METHOD ANDDEVICE”, “METHOD FOR HUMAN-ASSISTED RANDOM KEY GENERATION ANDAPPLICATION FOR DIGITAL WATERMARK SYSTEM”, and “METHOD FOR STEGA-CIPHERPROTECTION OF COMPUTER CODE”, “OPTIMAL METHODS FOR THE INSERTION,PROTECTION AND DETECTION OF DIGITAL WATERMARKS IN DIGITIZED DATA”.Recursive digital filters are efficient for applications dependent onprevious inputs and outputs and current inputs at a given time—a dynamicfilter. The z-transform makes possible high performance of time domaindigital filtering with implementation of recursive filters where signalcharacteristics are efficiently identified.

In one embodiment of the present invention, z-transform calculations areperformed as an intermediate processing step, prior to the actualencoding of a digital watermark into a sample stream. The Argent™digital watermark software, developed by The DICE Company, for example,uses a modular architecture which allows access to the sample stream andrelated watermark data at various stages of computation, and furtherallows modules to pass their results on (or back) to other modules.Z-transform calculations can be integrated into this processingarchitecture either directly in the CODEC module, which is responsiblefor encoding information to a series of samples, or decoding it fromthem, or as a FILTER module, which provides other modules withinformation on how specific types of filters will affect the samplestream. During processing, a series of sample frames are separated intogroupings called “windows”. Typically the groupings are comprised ofcontiguous series of samples, but this need not be the case. Any logicalarrangement might be handled. Each sample window comprises a finiteduration two-sided signal, a special case for z-transform calculationsdiscussed above.

Each window may then be fed to a z-transform calculator (in a FILTER orCODEC module) which derives phase composition information from thesignal using a z-transform algorithm. This information summarizesestimates of any regular phase components of the signal. Note thatwindows may be dynamically adjusted to be longer or shorter duration, orthey may be computed in an overlapping fashion, with information aboutadjacent windows and their z-transforms being considered with regard tothe current transform. Windows might have weightings applied to sampleframes in order to emphasize some portions or de-emphasize others. Usingthese additional modifications may help to smooth discontinuitiesbetween window calculations and provide a better average estimate overlonger portions of a signal.

The resulting z-transform information could be visualized by placingpoints of varying brightness or color (which corresponds to anamplitude) on the unit circle in the complex z-plane (the circlecentered at z=0.0, 0.0 with radius 1). These points symbolize recurrentsignal components at particular phases (where phase is determined by theangle of the line drawn between the point on the perimeter of the circleand its center). A deterministic approximation of the signal could thenbe reconstructed with all possible times represented by multiplyingphase by the number of revolutions about the circle. Positive angleincrements move forward in time, while negative increments movebackward. The phase components yielded by the z-transform are then usedto summarize and reproduce an estimate of the deterministic portion ofthe signal. Typically one may invert the z-transform calculations toproduce this estimate in terms of a series of wave amplitude samples. Bycalculating the error rate and location of such errors in the estimatedsignal versus the original, the system can determine exactly where asignal is “most non-deterministic,” which would constitute promisinglocations within the sample stream to encode watermark information. Notethat location could be construed to mean any combination of sample,frequency or phase information.

The process described above is, in principle, an inversion of the typeof process used for Linear Predictive Coding (LPC) and is a generalexample of “filter inversion” for optimal watermark planning. The typecalculations are performed in order to determine what parts of thesignal will survive the LPC process intact, and are thus good places toplace watermarks which are to survive LPC. In LPC, the deterministicportion of a signal is compressed and the non-deterministic portion iseither preserved as a whole with lossless compression or stochasticallysummarized and recreated randomly each time the “signal” is played back.

1. A method in the original method of using z-transform calculations to encode carrier signal independent data to a digital sample stream. 2-46. (canceled)
 47. A method for extracting a digital watermark from a content signal, comprising a) receiving a content signal; b) using linear predictive coding calculations to identify predictable and unpredictable components of said content signal,.said unpredictable-signal components being characterized by at least one of the following groups: i) a discrete series of digital samples, and ii) a discrete series of carrier frequency sub-bands of the content signal; and c) extracting the digital watermark from the unpredictable signal components of the content signal.
 48. The method of claim 47, wherein the content signal is an analog waveform.
 49. The method of claim 47, where the signal components are non-contiguous.
 50. The method of claim 47, where the content signal may first be decompressed before using linear predictive coding to identify signal components.
 51. The method of claim 47, where the location of at least a portion of the digital watermark is represented by at least one of the following: sample, frequency, phase or combinations thereof.
 52. The method of claim 47, wherein the step of extracting comprises: extracting the digital watermark based on one or more locations within said unpredictable signal components.
 53. The method of claim 47, wherein the signal components are identified using at least one of the following characteristics of the content signal: wave, amplitude, frequency, band energy, and phase energy.
 54. The method of claim 47, where the linear predictive coding calculations enables compression of the predictable signal components and at least one of the following: preservation of the unpredictable signal components or stochastic representation of the unpredictable signal components.
 55. The method of claim 47, where the digital watermark is accessible with a key.
 56. A method for extracting a digital watermark from a content signal, comprising a) receiving a content signal; b) using linear predictive coding calculations to identify predictable and unpredictable components of said content signal, said predictable signal components being characterized by at least one of the following group: i) a discrete series of digital samples, and ii) a discrete series of carrier frequency sub-bands of the content signal; and c) extracting the digital watermark from the predictable signal components of the content signal.
 57. The method of claim 56, wherein the content signal is an analog waveform.
 58. The method of claim 56, where the signal components are non-contiguous.
 59. The method of claim 56, where the content signal may first be decompressed before using linear predictive coding to identify signal components.
 60. The method of claim 56, where the location of at least a portion of the digital watermark is represented by at least one of the following: sample, frequency, phase or combinations thereof.
 61. The method of claim 56, wherein the step of extracting comprises: extracting the digital watermark based on one or more locations within said predictable signal components.
 62. The method of claim 56, wherein the signal components are identified using at least one of the following characteristics of the content signal: wave, amplitude, frequency, band energy, and phase energy.
 63. The method of claim 56, where the linear predictive coding calculations enables compression of the predictable signal components and at least one of the following: preservation of the unpredictable signal components or stochastic representation of the unpredictable signal components.
 64. A method of using linear predictive coding calculations to measure the desirability of particular locations in a sample stream in which to encode content signal independent data, including a digital watermark, comprising: receiving a sample stream; using linear predictive coding calculations to identify locations in said sample stream which would be desirable for encoding content signal independent data; and encoding said content signal independent data into said identified locations in said sample stream to produce an embedded sample stream.
 65. The method of claim 64, where the embedded sample stream is an arbitrarily close approximation of the sample stream.
 66. the method of claim 64, where the content signal independent data is accessible with a key. 